Christopher Makler
Stanford University Department of Economics
Econ 50 | Lecture 19
Exogenous Variables
Endogenous Variables
technology, f()
level of output, q
conditional
input demands
Cost Minimization
Isoquant
Isocost
lines
factor prices (w, r)
profit-maximizing output supply
Profit Maximization
output price, p
Total Revenue
Total Cost
profit-maximizing input demands
total cost
What is an agent's optimal behavior for a fixed set of circumstances?
Utility-maximizing bundle for a consumer
Profit-maximizing quantity for a firm
Profit-maximizing input choice for a firm
How does an agent's optimal behavior change when circumstances change?
Utility-maximizing bundle for a consumer
Profit-maximizing quantity for a firm
Profit-maximizing input choice for a firm
We will be analyzing a
competitive (price-taking) firm
TR
TC
MR
MC
Take derivative and set = 0:
Solve for \(q^*\):
SUPPLY FUNCTION
1. Total costs = cost of required inputs
2. Profit = total revenues minus total costs
3. Take derivative of profit function, set =0
1. Total revenue = value of output produced
2. Profit = total revenues minus total costs
3. Take derivative of profit function, set =0
1. Total revenue = value of output produced
2. Profit = total revenues minus total costs
3. Take derivative of profit function, set =0
"Keep producing output as long as the marginal revenue from the last unit produced is at least as great as the marginal cost of producing it."
"Keep producing output as long as the marginal revenue from the last unit produced is at least as great as the marginal cost of producing it."
"Keep hiring workers as long as the marginal revenue from the output of the last worker is at least as great as the cost of hiring them."
TR
TC
MRPL
MC
Take derivative and set = 0:
Solve for \(L^*\):
LABOR DEMAND FUNCTION
LABOR DEMAND FUNCTION
LABOR DEMAND FUNCTION
SUPPLY FUNCTION
the conditional labor demand
for the profit-maximizing supply:
The profit-maximizing labor demand is
Edge Case 1:
Multiple quantities where P = MC
Edge Case 2:
Corner solution at \(q = 0\)
"The supply curve is the portion of the MC curve above minimum average variable cost"
LONG RUN
SHORT RUN
LONG RUN
SHORT RUN
LONG RUN
SHORT RUN
What is the output elasticity of conditional labor demand in the short run and long run?
Intuitively, why this difference?
In the long run, the firm uses
both labor and capital to increase output;
in the short run, it only increases labor.
LONG RUN
SHORT RUN
LONG RUN
SHORT RUN
What is the price elasticity of supply
in the long run and short run?
Intuitively, why this difference?
In the long run, the firm can adjust its capital to keep its costs down; so its marginal cost rises less steeply, and its supply curve is flatter.
LONG RUN
Work with a partner:
How would the firm respond to a
6% increase in the wage rate in the long run?
pollev.com/chrismakler
How would the firm respond to a
6% increase in the wage rate in the long run?
A 6% increase in w decreases q by 3%.
and decreases by 6% (due to the -3% change in q),
for a total decrease of 9%.
K increases by 3% (due to the +6% change in w)
L decreases by 3% (due to the +6% change in w)
and decreases by 6% (due to the -3% change in q),
for a total decrease of 3%.
How would the firm respond to a
6% increase in the wage rate in the long run?
A 6% increase in w decreases q by 3%.
and decreases by 6% (due to the -3% change in q),
for a total decrease of 9%.
L decreases by 3% (due to the +6% change in w)
Note: we can calculate the LR profit-maximizing demand for labor:
A competitive firm takes input prices \(w\) and \(r\), and the output price \(p\), as given.
We can therefore characterize its optimal choices of inputs and outputs
as functions of those prices: the supply of output \(q^*(p\ |\ w)\),
and the demand for inputs (e.g. \(L^*(w\ |\ p)\)).
We can find the optimal input-output combination either by finding the optimal quantity of output and determining the inputs required to produce it, or to find the profit-maximizing inputs and determine the resulting output. These two methods are equivalent.
Profit is increasing when marginal revenue is greater than marginal cost, and vice versa.
In most cases, the profit-maximizing choice occurs where \(MR = MC\).
If \(p\) is below the minimum value of AVC, the profit-maximizing choice is \(q = 0\).
In which MR or MC is discontinuous, logic must be applied. (There is an old exam question on the homework that explores this...and this kind of thing often shows up on exams...)